Improving the performance of PINNs is an area of active research.
Several techniques for increasing the training stability have been proposed recently and many of them are available in software libraries [1]}, [2]}.
The closest to our approach is the idea of splitting the solution interval into multiple sub-intervals and fitting PINNs on each sub-interval separately [3]}.
Another related method [4]} proposes adaptive weights for the individual points that contribute to the PDE loss (REF ).
The point weights are calculated based on the cumulative PDE error for the preceding points. The idea is to zero out the effect of points that are far away from the initial conditions until the solution is approximated well on the points before them.
Work [5]} suggests that PINN training can be improved by better balancing of the weights for the loss terms (REF )–(REF ). [6]} proposes automatic annealing of the learning rate based on the statistics of the gradients.
Another important direction is finding neural network architectures that work better in PINNs. [7]} suggests using Fourier feature networks [8]} for solving PDEs. The method called SIREN [9]} utilizes periodic activation functions and adjusts the weight initialization scheme to work better with this type of activations.
There are also many specialized versions of PINNs developed to handle specific types of equations (see, e.g., [10]}, [11]}, [12]}).
